Show that 1+i^ 10 +i^ 20 +i^ 30 is a real number. - Vidyadip

Question

Show that $1+\text{i}^{10}+\text{i}^{20}+\text{i}^{30}$ is a real number.

✓

Answer

$1+\text{i}^{10}+\text{i}^{20}+\text{i}^{30}=1+\text{i}^{4\times2}\times\text{i}^2+\text{i}^{4\times5}+\text{i}^{4\times7}\times\text{i}^2$

$=1+1\times\text{i}^2+1+1\times\text{i}^2$

$=1-1+1-1$

$=0,$ which is real number.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Complex Numbers→Complex Numbers — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If P and Q are two sets such that P has 40 elements, $\text{P}\cup\text{Q}$ has 60 elements and $\text{P}\cap\text{Q}$ has 10 elements, how many elements does Q have?

Find the general solutions of the following equations:
$\tan\text{x}+\cot2\text{x}=0$

We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?

If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit?

Find the real numbers x and y if (x - iy) (3+ 5i) is the conjugate of -6 - 24i.

Solve: 27x² - 10x+ 1 = 0

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:

Exactly 3 girls?
At least 3 girls?
At most 3 girls?

Find the angle between X-axis and the line joining the points (3, -1) and (4, -2).

Solve: Sin 2x + sin 4x + sin 6x = 0.

Differentiate the following function with respect to x:

$\frac{\text{x}^2\cos\frac{\pi}{4}}{\sin\text{x}}$